Answer:
The maximum profit of $ 10277.32____ can be made when the selling price of the dog food is set to $ _34___ per bag.
Step-by-step explanation:
Profit = Revenue - Cost
P(x) = R(x) -C(x)
= -31.72x^2 + 2,030x -( -126.96x + 26,391)
Distribute the minus sign
= -31.72x^2 + 2,030x+126.96x - 26,391
Combine like terms
= -31.72 x^2 + 2156.96 x - 26391
This is a parabola. It is facing downwards. The maximum profits is at the vertex ( where the max is)
vertex = h = -b/2a = -(2156.96)/(2*-31.72) = -2156.96/-63.44=34
Evaluate P(x) at x=34 to determine the profit
P(34) = -31.72 (34)^2 + 2156.96 (34) - 26391
-36668.32+73336.64-26391
10277.32
The maximum profit of $10,243.32 can be made when the selling price of the dog food is set to $947.17. per bag.
1. Define the profit function: Profit [tex](\( P(x) \))[/tex] is calculated by subtracting the cost function [tex](\( C(x) \))[/tex] from the revenue function [tex](\( R(x) \)):[/tex]
[tex]\[ P(x) = R(x) - C(x) \][/tex]
2. Substitute the given revenue and cost functions:
[tex]\[ R(x) = -31.72x^2 + 2,030x \][/tex]
[tex]\[ C(x) = -126.96x + 26,391 \][/tex]
3. Plug in the revenue and cost functions into the profit function:
[tex]\[ P(x) = (-31.72x^2 + 2,030x) - (-126.96x + 26,391) \][/tex]
[tex]\[ P(x) = -31.72x^2 + 2,156.96x - 26,391 \][/tex]
4. Find the x-coordinate of the vertex of the profit function:
The x-coordinate of the vertex is given by:
[tex]\[ x = \frac{-b}{2a} \][/tex]
where [tex]\( a = -31.72 \) and \( b = 2,156.96 \).[/tex]
[tex]\[ x = \frac{-2,156.96}{2*(-31.72)} \][/tex]
x ≈ 34
5. Calculate the maximum profit:
Substitute x ≈ 34 into the profit function:
P(34) ≈ [tex]-31.72(34)^2 + 2,156.96(34) - 26,391[/tex]
P(34) ≈ 10,243.32
6. Determine the selling price per bag that maximizes profit:
Plug x ≈ 34 into the revenue function to find the corresponding revenue:
[tex]\[ R(34)[/tex] ≈ [tex]-31.72(34)^2 + 2,030(34)[/tex]
[tex]\[ R(34)[/tex] ≈ [tex]32,183.68[/tex]
Divide the revenue by the quantity x ≈ 34 to find the selling price per bag:
[tex]\[ \text{Selling price per bag}[/tex] ≈ [tex]\frac{32,183.68}{34}[/tex] ≈ [tex]947.17[/tex]
So, the maximum profit is approximately $10,243.32, and the selling price per bag that maximizes profit is approximately $947.17.
Find the slope give the points (-7,-4) and (5,8)
Answer:
1
Step-by-step explanation:
gradient = (8-(-4)) / (5-(-7)) = 12 / 12 = 1
Answer:
1
Step-by-step explanation:
(-7,-4)
x1 y1
(5,8)
x2 y2
8-(-4)/5-(-7) = 12/12 = 1
v
15 10
In the circle shown, chords AC and BD intersect at E. If AE = 6, EC =
12, and DE = 18. How long is
BE
Answer:
BE is 4 units long
Step-by-step explanation:
Data
AE = 6EC = 12DE = 18Given that chords AC and BD intersect at E, then the following equation must be satisfied:
AE * CE = DE * BE
Replacing with data and isolating BE:
6*12 = 18*BE
BE = 6*12/18
BE = 4
Write 18.4 as a fraction in lowest terms
Answer:
Divide each side of 18/4 by 2 to get 9/2.
Answer:
184/10
Step-by-step explanation:
You have to delete the comma (,) so, by doing ×10 you have 18,4 -> 184. By doing ÷10 you have a fraction: 184/10 that is equal to 18.4
2.184÷0.7 pls help STAT
Answer:
3.12
Step-by-step explanation:
Hellllpppp Pleaseeeeee
Answer:
Statement 1 & Statement 3
Step-by-step explanation:
4 ÷ 10/3
4 × 3/10
12/10
6/5
f(x + 1) = (6/5) × f(x)
f(x) = (10/3) × (6/5)^(x-1)
f(x) = (10/3) × (5/6) × (6/5)^x
f(x) = (25/9) × (6/5)^x
The domain is all natural numbers and the range is real numbers
Step-by-step explanation:
Step 1: Find the correct answer
Option A is correct because if you plug in the numbers...
[tex]f(0 + 1) = \frac{10}{3}[/tex] → [tex]f(1)=\frac{10}{3}[/tex]
[tex]f(1 + 1) = \frac{6}{5} * \frac{10}{3}[/tex] → [tex]f(2)=4[/tex]
[tex]f(2 + 1) = \frac{6}{5} * \frac{4}{1}[/tex] → [tex]f(3) = \frac{24}{5}[/tex]
[tex]f(3 + 1) = \frac{6}{5} * \frac{24}{5}[/tex] → [tex]f(4) = \frac{144}{25}[/tex]
Also, Option C is correct because if you plug in the numbers...
[tex]f(1) = \frac{10}{3}(\frac{6}{5})^(^1^-^1^)[/tex] → [tex]f(1) = \frac{10}{3} * 1[/tex] → [tex]f(1)=\frac{10}{3}[/tex]
[tex]f(2) = \frac{10}{3}(\frac{6}{5})^(^2^-^1^)[/tex] → [tex]f(2) = \frac{10}{3}*\frac{6}{5}[/tex] → [tex]f(2) = 4[/tex]
[tex]f(3) = \frac{10}{3}(\frac{6}{5})^(^3^-^1^)[/tex] → [tex]f(3) = \frac{10}{3}*\frac{36}{25}[/tex] → [tex]f(3) = \frac{24}{5}[/tex]
[tex]f(4) = \frac{10}{3}(\frac{6}{5})^(^4^-^1^)[/tex] → [tex]f(4) = \frac{10}{3} * \frac{216}{125}[/tex] → [tex]f(4) = \frac{144}{25}[/tex]
The reason why option B is not correct is because when you plug in a number, the output is incorrect. The reason why Option D is not correct is because the domain does not include negative numbers which means that the domain is all natural numbers. The reason why Option E is not correct is because the range is all real numbers and not just natural/positive numbers.
Answer: Options A, C
What is the number of ordered pairs (x,y) that are solutions to
4x+5y=2017
where both x and y are positive integers?
Answer:
Step-by-step explanation:
An ordered pair is a pair of coordinates on a graph that satisfy a particular equation.
From our question, the given equation is
4x + 5y = 2017
5y = 2017 - 4x
y = (2017 - 4x) / 5
but (x,y) are positive integers meaning that x and y > 0
when x = 1, y = (2017 - 4) /5
y = 2013/5
=402.6
Hence (x.y) = (1. 402.6) which is not a solution to the equation
when x = 2 , y = (2017 -8) /5
y = 2009/ 5 = 401.8
(x,y) = (2, 401.8) which is not a solution to the equation
when x = 3 , y = (2017 - 12)/ 5
y = 2005/5 = 401
(x, y) = (3, 401) which is a solution to the equation
when x =5 , y = (2017 - 20) / 5
y = 1997/5 = 399.4
(x,y) = (5, 399.4) which is not a solution to the equation
There are 216 one-inch cubes stacked in such a way as to create a larger cube. How many one-inch cubes are on a single edge of the larger cube?
Final answer:
To find out how many one-inch cubes are on a single edge of the larger cube formed by stacking 216 cubes, take the cube root of 216, which is 6. Therefore, each edge has 6 one-inch cubes.
Explanation:
If there are 216 one-inch cubes stacked to form a larger cube, we need to determine how many cubes are along each edge of this larger cube. The volume of a cube is calculated as length × width × height, and since all sides of a cube are equal, we can say that the length, width, and height are all the same. Therefore, to find the length of one side, we take the cube root of the volume. The cube root of 216 is 6, meaning each edge of the larger cube is composed of 6 one-inch cubes.
1) Simplify and write your answer with one base and one exponent.
6^-5 x 6^2
Answer:
6^-3
Step-by-step explanation:
6^-5 * 6^2
6 * 6 = 6^(-5 +2)
6^-3
I thing I may be wrong
In the equation 2x + 7 = 21, what is the value of x?
A.7 B.9 C.11 D.14
What is the domain of the profit function P=6t+10s?
Answer:A
Step-by-step explanation:
The required profit function is defined for all s and t greater than or equal to zero. Option A is correct.
What are functions?Functions are the relationship between sets of values. e g y=f(x), for every value of x there is its exists in a set of y. x is the independent variable while Y is the dependent variable.
Here,
The profit function P=6t+10s represents the profit made by a company based on the number of units of two products: t units of product 1 and s units of product 2.
In general, the domain of the profit function depends on the specific context of the problem, but in the problem, we have no constraints so the domain of the profit function would be all real values for s and t greater than or equal to zero.
Thus, the required profit function is defined for all s and t greater than or equal to zero. Option A is correct.
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trevors baseball card collection consists of 228 cards. this is 4 times as many cards as ming has. how many baseball cards are in mings collection'
Answer:
57
Step-by-step explanation:
If Trevor has 4 times more cards then Ming and Trevor has 228 cards you would divide 228 by 4 to get the number of cards ming has.
228 divided by 4 is 57
Which system of equations could be graphed to solve the equation below?
log Subscript 0.5 Baseline x = log Subscript 3 Baseline 2 + x
y 1 = StartFraction log 0.5 Over x EndFraction , y 2 = StartFraction log 3 Over 2 + x EndFraction
y 1 = StartFraction log x Over log 0.5 EndFraction, y 2 = StartFraction log 2 + x Over log 3 EndFraction
y 1 = StartFraction log 0.5 Over log 3 EndFraction, y 2 = StartFraction log x Over log 2 + x EndFraction
y 1 = StartFraction log x Over log 0.5 EndFraction, y 2 = StartFraction log 2 Over log 3 EndFraction + x
Answer:
y 1 = StartFraction log x Over log 0.5 EndFraction, y 2 = StartFraction log 2 Over log 3 EndFraction + x
Step-by-step explanation:
To solve the log equation, the appropriate system of equations is y₁ = log₀.₅ x and y₂ = log₃(2+x) as these correspond to the format of the original log equation, where we can equate the two and solve for x.
Explanation:To solve the equation log₀.₅ₓ = log₃ (2+x), we can rewrite it in a form that helps us find a system of equations.
First, apply the change of base formula for logarithms:
log ab/ log ac = log cb.
Using this formula, we can rewrite the given equation as:
log 0.5x / log₀.₅ 10 = log₃(2+x) / log₃10
Now, we can create a system of equations with the following relationships:
y₁ = log₀.₅ x / log₀.₅10
y₂ = log₃(2+x) / log₃10
Therefore, the correct choice is:
y₁ = logₓ/log₀.₅ , y₂= log(2+x)/ log 3
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factor this four term polynomial: 4x^4-2x^3-6x+3
Answer:
( 2 x − 1 ) ( 2 x↑ 3 − 3)
Step-by-step explanation:
The arrow indicates that the 3 is an exponent
Also Mark me brainliest!
How is the binomial 2x^2y-4xy^3 expresses in factores form
Answer:
2xy • (x - 2y2)
Step-by-step explanation:
STEP 1
:
Equation at the end of step 1
((2 • (x2)) • y) - 22xy3
STEP 2
Equation at the end of step
(2x2 • y) - 22xy3
STEP 3
STEP 4
:
Pulling out like terms
4.1 Pull out like factors :
2x2y - 4xy3 = 2xy • (x - 2y2)
Trying to factor as a Difference of Squares:
4.2 Factoring: x - 2y2
Theory : A difference of two perfect squares, A2 - B2 can be factored into (A+B) • (A-B)
Proof : (A+B) • (A-B) =
A2 - AB + BA - B2 =
A2 - AB + AB - B2 =
A2 - B2
Note : AB = BA is the commutative property of multiplication.
Note : - AB + AB equals zero and is therefore eliminated from the expression.
Check : 2 is not a square !!
Ruling : Binomial can not be factored as the difference of two perfect squares.
What is the area of r=5
Answer:
if you need the circumferance of a circle with a radious of 5, then it should be 31.42.
Step-by-step explanation:
Answer:
25pi or 78.5 units^2
Step-by-step explanation:
A = pi r^2
A = 25pi or 78.5
What is the perimeter and area of the trapezoid?
Answer:
Perimeter = sum of length of all sides = 8 + 3 + 10 + 11 = 32
Area = (base1 + base2) x height/2 = (3 + 11) x 7/2 = 49
Hope this helps!
:)
Did you hear about the lettuce and tomato race? The lettuce was a head and the tomato tried to ketchup.
Answer:
bruh
Step-by-step explanation:
b r u h
Roxane is designing a new cake box for a local bakery. The template for the cake box is shown above. When the template is folded along the dotted lines, it makes a box with a length of 42 centimeters, a width of 20 centimeters, and a height of 10 centimeters.
How much paperboard is needed to make the cake box?
A.
2,080 square centimeters
B.
1,462 square centimeters
C.
2,920 square centimeters
D.
1,460 square centimeters
Answer:
Area of rectangle box = 2,920 CM²
Step-by-step explanation:
Given:
Length = 42 Cm
Width = 20 Cm
Height = 10 Cm
Find:
Total area required to make box = ?
Computation:
Area of rectangle box = 2[LB + BH + HL]
Area of rectangle box = 2[(42 × 20) + (20 × 10) + (10 × 42)]
Area of rectangle box = 2[(840) + (200) + (420)]
Area of rectangle box = 2[1,460]
Area of rectangle box = 2,920 CM²
Which statement is true?
Only some squares are rectangles. Rectangles have 4 right angles. Therefore, only some squares have 4 right angles.
Only some squares are rectangles. Rectangles have 4 sides that are the same length. Therefore, only some squares have 4 sides that are the same length.
All squares are rectangles. Rectangles have 4 sides that are the same length. Therefore, all squares have 4 sides that are the same length.
All squares are rectangles. Rectangles have 4 right angles. Therefore, all squares have 4 right angles.
Answer:
All squares are rectangles. Rectangles have 4 right angles. Therefore, all squares have 4 right angles.
Step-by-step explanation:
The old math saying: "Every square is a rectangle, but not all rectangles are squares."
What makes a rectangle a rectangle is that it has four right angles.
A square also has four right angles. Therefore, a square is a type of rectangle.
What makes the other answers wrong:A rectangle does not have equal lengths on all four sides like a square does.
A square MUST have four right angles for it to be a square.
Brainiliest Appreciated.
Question:
A. 1) Only some squares are rectangles. 2) Rectangles have 4 right angles. 3) Therefore, only some squares have 4 right angles.
B. 1) Only some squares are rectangles. 2) Rectangles have 4 sides that are the same length. 3) Therefore, only some squares have 4 sides that are the same length.
C. 1) All squares are rectangles. 2) Rectangles have 4 sides that are the same length. 3) Therefore, all squares have 4 sides that are the same length.
D. 1) All squares are rectangles. 2) Rectangles have 4 right angles. 3)Therefore, all squares have 4 right angles.
Answer:
All squares are rectangles. Rectangles have 4 right angles. Therefore, all squares have 4 right angles.
Step-by-step explanation:
Let's go by process of elimination. Starting with A.
A. 1) Only some squares are rectangles. 2) Rectangles have 4 right angles. 3) Therefore, only some squares have 4 right angles.
You can already tell that it's incorrect just looking at sentence 1). All squares are rectangles because a rectangle is:
1. Quadrilateral.
2. Two pairs of parallel sides.
3. Four right angles.
Sentence 2) is correct because Rectangles have 4 right angles. But sentence 3) is incorrect because all squares have 4 right angles.
Down to B.
B. 1) Only some squares are rectangles. 2) Rectangles have 4 sides that are the same length. 3) Therefore, only some squares have 4 sides that are the same length.
Same thing in the first sentence as A . Sentence 1) is incorrect since all squares are rectangles. Sentence 2) is also incorrect because Rectangles do not have the same lengths on all four sides. Only two sides are the same in length. The sides that are the same are the two sides across from each other. Sentence 3) is also incorrect since all squares have 4 sides that are the same length.
Moving down again to C.
C. 1) All squares are rectangles. 2) Rectangles have 4 sides that are the same length. 3) Therefore, all squares have 4 sides that are the same length.
Sentence 1) is correct. All squares are rectangles. Sentence 2) is incorrect because not all sides are the same length. Sentence 3) is correct because all squares have 4 sides that are the same length.
Down to D. (The correct answer.)
D. 1) All squares are rectangles. 2) Rectangles have 4 right angles. 3)Therefore, all squares have 4 right angles.
Sentence 1) is correct because all squares are in fact, rectangles. here is a fact about squares:
"A square is a quadrilateral with all four angles, right angles, and all four sides of the same length. So a square is a special kind of rectangle, it is one where all the sides have the same length. Thus every square is a rectangle because it is a quadrilateral with all four angles right angles."
Sentence 2) is also correct because all rectangles have four right angles. Here are some more facts about rectangles:
"All rectangles are parallelograms, but all parallelograms are not rectangles.
The diagonals of a rectangle divide the rectangle into four triangles.
Every square is a rectangle, but every rectangle is not a square."
Sentence 3) is correct. All squares have 4 right angles. Therefore, Option D. would be your correct answer.
Liz flips a coin 90 times. The coin lands heads up 54 times and tails up 36 times. Complete each statement.
The theoretical probability of the coin landing heads up is
Answer:
1/2 or 50%
Step-by-step explanation:
Please check if that is correct. But generally there are two sides so half of the times it should be heads.
Hope this helps.
Which weighs more: a pumpkin that weighs 3.2 kilograms, Or a cat that weighs 9 pounds? Note 1 pound is about 0.45 kilograms
Answer:
The cat weighs more.
Step-by-step explanation:
The cat weighs 4.08 kilograms and the pumpkin weighs 3.2 kilograms.
9lbs=4.08 kilograms.
Hope this helps : )
The body that weighs more, based on its relative mass is the cat.
The cat weighs 9 pounds and the pumpkin weighs 3.2 kilograms.
To know which weighs more, they need to be weighed in the same units.
Convert the cat to kilograms:
= Number of pounds x Pounds to kilograms
= 9 x 0.45
= 4.05 kg
The cat therefore weighs more than the pumpkin.
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The slope-intercept form of the equation of a line that passes through the point (4, -3) is y=-3x+5. What is the point-slope form of the
equation for this line?
Point-Slope Form:y- y1=m(x-x1)
y-3--1/3x+4)
y-4--1/3 (X - 3)
y-4--1/3(x+3)
y+ 3 = -1/3 (x-4)
Answer:
y+ 3 = -1/3 (x-4)
Step-by-step explanation:
Simply plug in the values using (4, -3)
4 = x₁
-3 = y₁
Now one rule to keep in mind when plugging it in, since a negative and a negative make a positive, you have to add three instead of subtracting it.
Answer:
I think the answer is y+ 3 = -1/3 (x-4)
Step-by-step explanation:
PLEASE HELP ITS AN EMERGENCY
Answer:
the answer is d
Step-by-step explanation:
You might need:
Calculator
Yasemin deposited $1000 into a savings account.
The relationship between the time, t, in years, since the account was first opened, and Yasemin's account
balance, B(t), in dollars, is modeled by the following function.
B(t) = 1000. 20.03
How many years will it take for Yasemin's account balance to reach $1500?
Round your answer, if necessary, to the nearest hundredth.
Answer:
The number of years it will take for Yasemin's account balance to reach $1500 is 13.52 years.
Step-by-step explanation:
Where the model of the relationship between the time, t, in years, since the account was first opened and the and the balance in Yasemin's account is presented as follows;
[tex]B(t) = 1000 \times e^{(0.03 \times t)}[/tex]
To find find out how many years it will take for Yasemin's account balance to reach $1500, we substitute B(t) = $1500 since we are told that after the years his account balance became $1500 as follows;
[tex]\$ 1500 = 1000 \times e^{(0.03 \times t)}[/tex]
We now solve for t
[tex]\$ 1500 = 1000 \times e^{(0.03 \times t)}\\\\\frac{1500 }{1000 } = e^{(0.03 \times t)}\\1.5 = e^{(0.03 \times t)}\\\\ln(1.5) = ln (e^{(0.03 \times t)})\\\\ln(1.5) = (0.03 \times t) \times ln (e)\\\\\therefore ln(1.5) = (0.03 \times t) \\\\t = \frac{ln(1.5)}{0.03 } = 13.52 \ years[/tex]
The number of years it will take for Yasemin's account balance to reach $1500 = 13.52 years.
Help with this plzzzzzz
Answer:
C. 11:16 AM
Step-by-step explanation:
Subtract 42 minutes from 58, which is 16. To find out what hour, you subtract by 3. When you do subtract, the answer is 11 AM.
Hope this helps :)
hi i need help with this question
Answer:
[tex]a)5 \\ \: \: \: \: \: \: 8 \\ \: \: \: \: \: 11[/tex]
[tex]b)32[/tex]
Step-by-step explanation:
[tex]a)3n + 2 \\ 3 \times 1 + 2 = 5 \\ 3 \times 2 + 2 = 8 \\ 3 \times 3 + 2 = 11[/tex]
[tex]b)3n + 2 \\ 3 \times 10 + 2 = 32[/tex]
I'd appreciate if you rate my answer and give a thanks.
Check all of the correct names for the object pictured below.
O
O
B. EF
O
c. FE
O
D. FE
OE. EF
O
Answer:
A. & F.
Step-by-step explanation:
Answer:
A. & F.
Step-by-step explanation:
Evaluate the radical. 27−−√3 Enter your answer in the box.
Answer:
3
Step-by-step explanation:
took the test :p
The radical evaluation should be 3.
Calculation of the evaluation of the radical form:We know that the cube of 3 is 27
basically in this, no square roots, cube roots should be simplified.
So based on this, the radical evaluation should be 3.
Therefore, we can conclude that The radical evaluation should be 3.
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Olivia ordered a shirt online that cost her $38 total.
The package arrived late so the seller took 16% off
the price. How much did she end up paying?
I NEED UT TODAY
Answer:
$6.08
Step-by-step explanation:
38 x 0.16
equals $6.08
Answer:
$31.92
Step-by-step explanation:
Find 16 percent of 38
38*.16= 6.08
subtract
38-6.08= 31.92
How are percents related to rates?
Answer:
A percentage is defined as the ratio of two numbers times 100.
Answer:Example: 1 divided by 2 is 0.5 or 50%. An interest rate is expressed as a percentage or as a point. ... A percentage is defined a the ratio of 2 numbers times 100 (percent is Latin for per one hundred). Example: 1 divided by 2 is 0.5 or 50%.
Step-by-step explanation: